Min Force Req !

Two hemispheres of radius \(R\) combined together by two minimum forces '\(F\)' to form a sphere (completely filled with water) as shown in figure. A small pin hole of radius \(a\) at top of the sphere as shown in figure. If the system is in equilibrium at \(\tan \theta = \frac{x}{2}\) . Find the value of \(x\).

(Gravity is present and no other support is given to hemispheres)

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